Problem: Express this product in scientific notation: $(6.40\times 10^{-4})\times (4.00\times 10^{-2})$
Start by collecting like terms together. $= (6.40\times 4.00) \times (10^{-4}\times 10^{-2})$ When multiplying exponents with the same base, add the powers together. $= 25.6 \times 10^{-4\,+\,-2}$ $= 25.6 \times 10^{-6}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $25.6$ is the same as $2.560 \times 10$ $ = {2.560 \times 10} \times 10^{-6} $ $= 2.560\times 10^{-5}$